Probabilities are always axiomatizable

2025/10/31 by Gyenis, Zalán
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2511.00228

Abstract

In this paper we study the interaction between logic and probability. In particular, we show that the convex hull of evaluations of a broad class of logics is always effectively axiomatizable. We define a Birkhoff-style calculus for probability axioms for which compactness, and finite completeness is proved. We give example for a logic for which probabilities are not finitely axiomatizable.

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